Strong solutions to semilinear SPDEs

Martina Hofmanova (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We study the Cauchy problem for a semilinear stochastic partial differential equation driven by a finite-dimensional Wiener process. In particular, under the hypothesis that all the coefficients are sufficiently smooth and have bounded derivatives, we consider the equation in the context of power scale generated by a strongly elliptic differential operator. Application of semigroup arguments then yields the existence of a continuous strong solution.

Mots clés: Stochastic partial differential equations; strongly elliptic differential operator; strongly continuous semigroup

Domaines: Equations aux dérivées partielles [math.AP]; Probabilités [math.PR]

Martina Hofmanova. Strong solutions to semilinear SPDEs. Nonlinear Differential Equations and Applications, 2013, 20 (3), pp.757-778. ⟨10.1007/s00030-012-0178-x⟩. ⟨hal-00668272⟩